Helicities in Geophysics, Astrophysics, and Beyond

✍ Scribed by Kirill Kuzanyan (editor), Nobumitsu Yokoi (editor), Manolis K. Georgoulis (editor), Rodion Stepanov (editor)

• Publisher: American Geophysical Union
• Year: 2023
• Tongue: English
• Leaves: 267
• Series: Geophysical Monograph Series
• Edition: 1
• Category: Library

✦ Synopsis

Presents cutting-edge studies of helicities from different research fields

Helicities play essential roles in numerous geophysical, astrophysical, and magnetohydrodynamic phenomena, thus are studied from various disciplinary viewpoints.

Helicities in Geophysics, Astrophysics, and Beyond draws together experts from different research fields to present an interdisciplinary and integrated approach to helicity studies. This synthesis advances understanding of the fundamental physical processes underlying various helicity-related phenomena.

Volume highlights include:

• Concise introduction to fundamental properties of helicities
• Recent developments and achievements in helicity studies
• Perspectives from different fields including geophysics, space physics, solar physics, plasma physics, atmospheric and nonlinear sciences
• A cohesive mathematical, physical, observational, experimental, and numerical strategy for helicity studies
• A synthesized framework for the application of helicity to real-world problems

The American Geophysical Union promotes discovery in Earth and space science for the benefit of humanity. Its publications disseminate scientific knowledge and provide resources for researchers, students, and professionals.

✦ Table of Contents

fmatter
Title Page
Copyright
Contents
List of Contributors
Preface
ch1
Chapter 1 Introduction to Field Line Helicity
1.1 Definitions of Field Line Helicity
1.1.1 Definitions of Field Line Helicity for Closed Volumes
1.1.2 Definitions of Field Line Helicity for Open Volumes
1.1.3 Relative Field Line Helicity
1.2 Ideal Evolution
1.2.1 Simple Examples
1.2.2 Application to the Global Solar Corona
1.2.3 Application to Solar Active Regions
1.3 Non‐Ideal Evolution
1.3.1 Evolution Equation for Non‐Null Magnetic Fields
1.3.2 Application to Turbulent Magnetic Relaxation
References
ch2
2.1 Introduction
2.2 Relative Helicity
2.3 Magnetic Winding
2.3.1 Winding Helicity
2.3.2 Separating Out the Topology
2.3.3 Magnetic Winding Flux
2.4 Applications
2.4.1 Theoretical Examples
2.4.2 Solar Observations
2.5 Brief Historical Notes
References
ch3
3.1 Introduction
3.2 Helicity: Definition and Properties
3.3 Theoretical Analysis of Helicity Effects in Inhomogeneous Turbulence
3.3.1 Equations for Mean Fields and Fluctuation Fields
3.3.2 Statistical Analytical Theory for Inhomogeneous Turbulence
3.3.3 Analytical Expressions for Reynolds Stress and Vortex‐Motive Force
3.4 Turbulence Modeling with Helicity
3.4.1 Choice of One‐Point Statistical Quantities
3.4.2 Helicity Turbulence Model
3.5 Application to Swirling Flow
3.5.1 Swirling Flows
3.5.2 Characteristics of Turbulent Swirling Flow
3.5.3 Conventional Turbulence Model for Swirling Flow in a Straight Pipe
3.5.4 Analysis of Turbulent Swirling Flow with the Helicity Turbulence Model
3.6 Large‐Scale Flow Generation by Inhomogeneous Helicity
3.6.1 Vortex Dynamos
3.6.2 Simple Argument on the Origin of Flow Generation Due to the Helicity Effect
3.6.3 Numerical Validation of Global Flow Generation Due to the Helicity Effect
3.6.4 Possible Applications in Spherical Geometry
3.7 Summary and Conclusion
Acknowledgments
References
ch4
Chapter 4 Observations of Magnetic Helicity Proxies in the Solar Photosphere: Helicity With Solar Cycles
4.1 Introduction
4.2 Magnetic Helicity from Observations
4.2.1 Early Morphological Observations of Helical Patterns in the Solar Atmosphere
4.2.2 Magnetic Helicity from Solar Vector Magnetic Fields
4.3 Electric Current Helicity from Observations
4.3.1 Helicity from Solar Vector Magnetic Fields
4.3.2 Magnetic Helicity with Solar Cycles
4.4 Magnetic Helicity Injection on the Solar Surface
4.4.1 Magnetic Helicity Injection Inferred from Moving Magnetic Structures
4.4.2 Magnetic Helicity Injection with Solar Cycles
4.5 Magnetic Helicity as an Index in the High Solar Atmosphere
4.5.1 Hemispheric Distribution of Helical Coronal Soft X‐Ray Loops
4.5.2 Helicity with Solar Flare Cycles
4.6 Questions about Solar Dynamos with Observation of Magnetic Helicity
4.7 Discussion
Acknowledgments
References
ch5
5.1 Introduction
5.2 Magnetic Chirality of Solar Filaments
5.2.1 Fibril Orientation
5.2.2 Coronal Cells
5.2.3 Filament Drainage Brightening
5.3 Structural Chirality of Solar Filaments
5.4 Magnetic Configuration of Solar Filaments
5.5 Future Prospects
Acknowledgments
References
ch6
6.1 Introduction
6.2 Basic Concepts and Formulations
6.3 Methods of Helicity Estimation
6.3.1 Volume Helicity
6.3.2 Magnetic Helicity Flux
6.4 Practical Applications
6.4.1 Temporal Variation
6.4.2 Statistical Trends
6.4.3 Magnetic Tongues: A Proxy for the Helicity Sign
6.5 Numerical Models
6.5.1 Coronal Field Reconstructions
6.5.2 Idealized Simulations
6.6 Summary and Discussion
Acknowledgments
References
ch7
7.1 Introduction
7.2 The Parker Model as a Guide
7.3 Evaluating Magnetic Helicity
7.3.1 Uncurling the Vector Potential
7.3.2 Reduced Magnetic Helicity
7.3.3 Caveats
7.4 Helicity Profile in the Solar Wind
7.4.1 Reduced Helicity Spectra
7.4.2 Wave Picture of Magnetic Helicity
7.4.3 Scale and Hemispheric Dependencies
7.4.4 Solar Cycle Dependence
7.5 Summary and Outlook
Acknowledgements
References
ch8
8.1 Introduction
8.2 Theoretical Background
8.2.1 Mean Spin of the Electron Gas in an External Magnetic Field
8.2.2 Approximate Description of Chiral Plasma Based on Berry Phase Evolution
8.2.3 Electric Current and the Adler Anomaly in Inhomogeneous Matter Accounting for Electroweak Interaction
8.3 Astrophysical Applications
8.3.1 Quantum Surface Correction to the Chiral Anomaly in a Finite Volume of a Neutron Star
8.3.2 Magnetic Helicity Evolution as the Averaged Spin Flux through the Boundary of a Domain
8.3.3 Evolution of Magnetic Helicity in NSs
8.3.4 Magnetic Helicity Flow through the Equator of a Rotating NS
8.4 Conclusion
References
ch9
9.1 Introduction
9.2 Open Linking and Writhe
9.2.1 Fuller and Closures
9.2.2 Net Winding and the Polar Writhe
9.2.3 Helical‐to‐Loop Transition and Plectoneme Formation
9.2.4 Writhing as a Point of View
9.3 Bounding the Writhe of Proteins
9.3.1 Introduction to Protein Knotting
9.3.2 A Note on Downsampling Proteins
9.3.3 Borrowing from Solar Physics, Again
9.3.4 Applying Polar Writhe to Proteins
References
ch10
10.1 Introduction
10.2 General Information on Helicity
10.3 Helicity in Dynamic Atmospheric Processes
10.4 Helical Turbulence in the Earth's Atmosphere
10.5 Concluding Remarks and Outlook
Acknowledgments
References
ch11
Chapter 11 Effects of P-Noninvariance, Particles, and Dynamos
11.1 Introduction
11.2 Seed Magnetic Fields
11.3 Mirror Asymmetry and Helicity
11.4 Mean‐Field Dynamos in Relativistic Plasmas
11.4.1 Origin and Evolution of Alpha in the AMHD
11.4.2 The Influence of Turbulent Motion the CME in the Early Universe
11.4.3 Nascent Neutron Stars, Mirror Asymmetry, and Strong Magnetic Fields
11.5 Dynamo Driven by Neutrino Asymmetry in the Early Universe
11.6 Conclusions and Discussion
References
ch12
12.1 Introduction
12.2 Conservation of Helicity
12.3 Relaxation Equilibrium State
12.4 Field Relaxation Constraints
12.5 Plasma Stability
12.5.1 Solar Eruptions
12.5.2 Toroidal Fusion Plasma Fields
12.5.3 Numerical Experimental Evidence
12.6 Galactic and Intergalactic Media
12.6.1 Observations
12.6.2 Kelvin‐Helmholtz Instability
12.7 Helical Intergalactic Bubbles
12.7.1 Numerical Experiment
12.7.2 Helicity as a Stabilizer
12.8 Conclusions
Acknowledgments
References
ch13
13.1 Introduction
13.2 Kink Instability and Relaxation in the Solar Corona
13.2.1 Relaxation in Kink‐Unstable Flux Ropes
13.2.2 Observable Signatures of Energy Release in Flux Ropes
13.3 Merging Flux Ropes
13.3.1 Flux Rope Merging in Spherical Tokamaks
13.3.2 Heating Avalanches in the Solar Corona
13.4 Discussion and Conclusions
Acknowledgments
References
ch14
14.1 Introduction
14.2 Fourier Diagnostics and Shell‐to‐Shell and Helical Transfers
14.2.1 Shells, Spectra, and Cospectra
14.2.2 Helical Triadic Interactions
14.2.3 Shell‐to‐Shell Transfers
14.3 Results from Previous Research in Incompressible MHD
14.4 Numerical Method
14.5 Results
14.5.1 Spectra and Alfvénic Balance
14.5.2 Shell‐to‐Shell Transfers
14.6 Summary and Conclusion
References
ch15
15.1 Introduction
15.2 Mean‐Field Dynamos
15.3 Dynamic Nonlinearity: Transport of Magnetic Helicity
15.4 Formation of Sunspots
15.5 Observations of Proxies of Magnetic Helicity in the Sun
15.5.1 Observation of Solar Vector Magnetic Fields
15.5.2 Computation of Current Helicity
15.6 Nonlinear Model of a Mean‐Field Dynamo and Dynamics of the Sunspot Number
15.7 The Effect of Magnetic Helicity Transport and Prediction of Solar Activity
15.8 The Mean Tilt of Sunspot Bipolar Regions
15.9 Concluding Remarks
Acknowledgments
References
ch16
16.1 Introduction
16.2 Importance of Kinetic Helicity in Dynamo Action
16.2.1 Helicity in Dynamo Simulations
16.2.2 Lack of a Satisfactory Explanation for Helicity Segregation outside the TC
16.3 Sources of Helicity
16.3.1 Evolution Equation
16.3.2 Body Forces and Flux of Helicity
16.3.3 Helical Waves
16.4 Recent Results from Numerical Simulations
16.4.1 Model Problems: Rapidly Rotating, Localized Buoyant Anomalies
16.4.2 Numerical Geodynamo Simulations
16.5 A Conjecture for Helicity Segregation in Dynamo Simulations
16.6 Conclusions and Future Scope
Acknowledgments
References
index